Digital signals are often filtered using a pulse shaping filter prior to transmission. This is typically done to contain the signal bandwidth and minimize intersymbol interference between signal components corresponding to different digital symbols. This is shown in FIG. 1, where symbols from a digital constellation corresponding to the information being modulated are passed though a pulse shaping filter. In FIG. 1, the digital data to be transmitted is mapped into a complex signal constellation in block 101. For example, the complex signal constellation used may be an M-ary QAM constellation; however other constellations are also used. The mapped constellation undergoes pulse shaping in a filter as shown in block 102. Several methods known in the art can be employed for pulse shaping. The filtered constellation signal is converted to a radio frequency, represented as block 103, for transmission over the ether.
An artifact of this signal generation provides an unintended feature that has been the focus of recent investigation. If the digital signal is passed through a multi-path channel, the channel output is an aggregate of delayed, possibly faded and phase shifted replicas of the original digital signal. In practice, this occurs if a multiplicity of reflections of the transmitted signal are contained in the received signal. The delays can either be absolute, if the time of arrival of the direct path signal is known, or could be relative delays between the multi-path components. If these multi-path signals are received at the antenna array, the received signal can be mathematically formulated as a space-time signal.
When the characteristics of the pulse shaping filter and the antenna array are known, a theory of signal processing can be applied to estimate the multi-path delays of the signal components and their particular directions of arrival. This signal processing analysis is referred to as space-time processing. Space-time processing is a group of techniques that may be applied to resolve the received space-time signals into a sum of faded space-time signals. Each of these space time signals corresponds to the particular angle of arrival and time delay of one of the original multi-path signal components.
It is advantageous to develop a mathematical description of the prior art technique to convey the manner in which multi-path delays and angle of arrival (“AOA”) are currently calculated to fully appreciate the distinctness of the to be disclosed subject matter. The prior art method is illustrated in FIG. 2.
A column vector rk denotes the received signal at antenna k of an antenna array with m antennas, where k=1,2, . . . m. An impulse response hk of the multi-path channel is derived from rk, represented in block 201. The derivation of the column vector hk can be achieved by various methods and implemented with signal processors through software and/or hardware.
If the source data associated with this received block is known, a simple means of extracting hk is via the delay matrix corresponding to this source data. The delay matrix Z is formed by stacking symbol shifted copies of the source data in rows to a depth that defines the extent of the desired impulse response and truncating its longer dimension to match the length of rk. An estimate of hk is given by: hk=(ZZH)−1Zrk.
Alternate means for estimating the impulse response may provide better or worse estimates, depending on the particular modulation format of the data, the block length, the fading characteristics of the multi-path channel and possibly other parameters. Some of these other methods are blind to the actual data transmitted, using properties of either the signal modulation and/or of the channel instead.
Having estimated the impulse response of the multi-path channel from the source to antenna k of the array, a vectorized space-time impulse response over the entire array is formed, in block 202, by stacking the individual impulse response estimate hk into a long column vector {right arrow over (I)}, given by:
      I    →    =            [                                                  h              1                                                            …                                                              h              k                                                            …                                                              h              m                                          ]        .  
Theoretically, {right arrow over (I)} can be expressed as
      I    =                            ∑                      i            =            1                    n                ⁢                  I          i                    +      N        ,where {right arrow over (I)} indexes the individual space-time impulse responses, i=1,2, . . . , n, of the distinct multi-path components and N is a noise vector.
Any particular Ii is of the form Ii=βiηa(θi){circle around (×)}g(τi) in which βi denotes the fade multiplier for the signal block, and η denotes the signal amplitude at the transmitter. a(θi) denotes the antenna response corresponding to a signal arriving from angle θi, {circle around (×)} denotes the Khatri-Rao product, and g(τi) denotes the pulse shaping waveform delayed by τi and sampled. This formation of an outer product and aggregate in the covariance matrix, is represented in block 203. The formation of the covariance matrix can be implemented with signal processors or other computer processors through software and/or hardware devices.
The vectors a and g can be expressed as:
                    a        ⁡                  (                      θ            i                    )                    =              [                                                                              a                  1                                ⁡                                  (                                      θ                    i                                    )                                                                                                                          a                  2                                ⁡                                  (                                      θ                    i                                    )                                                                                        …                                                                                            a                  m                                ⁡                                  (                                      θ                    i                                    )                                                                    ]              ,    and              g      ⁡              (                  τ          i                )              =                  [                                                            g                ⁡                                  (                                                                                    -                        l                                            ⁢                                                                                          ⁢                                              T                        s                                                              -                                          τ                      i                                                        )                                                                                                        g                ⁡                                  (                                                                                    -                                                  (                                                      l                            -                            1                                                    )                                                                    ⁢                                              T                        s                                                              -                                          τ                      i                                                        )                                                                                        …                                                                          g                ⁡                                  (                                                            l                      ⁢                                                                                          ⁢                                              T                        s                                                              -                                          τ                      i                                                        )                                                                    ]            .      
In the equation for g(τi), l denotes the sampling depth of the pulse shaping function and Ts is the sampling time.
Given this formation of the space-time impulse response, when the number of multi-path components is smaller than the dimension of the symbol sampled impulse response vector I, it is possible to estimate the multi-path delays τi and the multi-path arrival angles θi.
The prior art approach to estimating the delays and arrival angles relies on an explicit knowledge of the aggregate of all vectors:
      a    ⁡          (              θ        i            )        =      [                                                      a              1                        ⁡                          (                              θ                i                            )                                                                                      a              2                        ⁡                          (                              θ                i                            )                                                            …                                                                a              m                        ⁡                          (                              θ                i                            )                                            ]  for all angles θi. This aggregate is termed the array manifold, A. It is assumed that the pulse shaping function at the transmitter is known at the receiver. Denoting the aggregate of all vectors as
      g    ⁡          (              τ        i            )        =      [                                        g            ⁡                          (                                                                    -                    l                                    ⁢                                                                          ⁢                                      T                    s                                                  -                                  τ                  i                                            )                                                                        g            ⁡                          (                                                                    -                                          (                                              l                        -                        1                                            )                                                        ⁢                                      T                    s                                                  -                                  τ                  i                                            )                                                            …                                                  g            ⁡                          (                                                l                  ⁢                                                                          ⁢                                      T                    s                                                  -                                  τ                  i                                            )                                            ]  for all values of τi as the delay manifold, G , then the quantity K=A{circle around (×)}G represents the space-time manifold.
The observation that Ii is contained in K leads to a primary objective of space-time processing: searching the manifold K for weighted linear combinations of vectors Ii such that a best fit to the observed space-time impulse response {right arrow over (I)} is generated as shown in block 204. A variety of techniques may be applied for this purpose, such as Multiple Signal Classification (MUSIC), The Method of Alternating Projections (APM), etc, which can be implemented through software and/or hardware. Other mathematical descriptions for jointly estimating the angle of arrival (“AOA”) and time delays can be found in Ziskind, I., Wax, M., “Maximum likelihood localization of multiple sources by alternating projection”, IEEE Trans. Acoust., Speech, Signal Process. vol. 36, no. 2 (October 1988), 1553-1560; Van Der Veen, M, Papadias, C. B., Pautraj, A. J., “Joint angle and delay estimation” IEEE Communications Letters vol. 1-1 (January 1997), 12-14; Schmidt, R. O. “Multiple emitter location and signal parameter estimation” Proc. RADC Spectrum Estimation Workshop, (March 1999), 243-258; Young-Fang Chen, Michael D. Zoltowski “Joint Angle and Delay estimation of DS-CDMA communication systems with Application to Reduced Dimension Space-time 2D Rake Receivers”, IEEE Transactions on Signal Processing; Paulraj, A. J., Papadias, C. B., “Space-Time Signal Processingfor Wireless Communications”, IEEE Signal Processing Magazine, vol. 11 (November 1997), 49-83; Paulraj, A. J., Papadias, C. B., “Space-Time Signal Processingfor Wireless Communications: A Survey” Information System Laboratory, Stanford University; and Haardt, Brunner and Nossek “Joint Estimation of 2-D Arrival Angles, Propagation Delays, and Doppler Frequencies in Wireless Communications”; all of which are incorporated herein by reference.
An object of the disclosed subject matter is to obviate the deficiencies of the prior art by removing the dependency of the time delay estimates from the spatial and gain characteristics of an antenna array thus allowing multi-path delay estimates to be obtained for any generic antenna array. This object is achieved by recasting the array manifold in a spatially blind manner so as to be independent of the array characteristics.
It is another object of the disclosed subject matter to present an improved method for estimating the multi-path delays in a signal received at any k array element. The method includes estimating an impulse response at each k antenna, generating a space-time impulse response, and forming a covariance matrix and resolving the covariance matrix with a known antenna array manifold. Additionally, a novel improvement to known methods includes the step of resolving the covariance matrix with a fictitious antenna array manifold.
It is still another object of the disclosed subject matter to present a novel method for estimating the multi-path delays in a signal using a spatially blind antenna array. The method includes generating an impulse response hk for each antenna k in the antenna array and determining a vectorized space-time impulse response I over the antenna array. The method further includes creating a covariance matrix C, a fictitious manifold Af, where Af is spatially blind and independent of the array characteristics, and then resolving the covariance matrix C with the fictitious manifold Af to estimate the multi-path delays τi in a manner independent of the array characteristics.
It is yet another object of the disclosed subject matter to present a method of estimating the multi-path delays of a sequence of j blocks of a signal received at an antenna array comprising k antenna elements independently of the spatial array characteristics of the antenna array. The method includes deriving a channel impulse response estimates hj,k for each block j at each antenna k and determining a vectorized aggregate space-time impulse response I for each block j. The method includes the steps of forming an estimated covariance matrix for the sequence of j blocks, forming an array manifold Af void of spatial information; and then resolving the covariance matrix with the fictitious array manifold Af to determine the multi-path delays τi.
It is also an object of the disclosed subject matter to present a novel system for estimating the multi-path delays in a signal using a spatially blind antenna array. The system includes an antenna array, a means for generating an impulse response hk, a means determining a vectorized space-time impulse response I and a means for creating a covariance matrix C. The system also includes a means for creating a fictitious manifold Af, wherein Af is spatially blind and independent of the array characteristics; and a means for resolving the covariance matrix C with the fictitious manifold Af to estimate the multi-path delays τi independent of the array characteristics.
These objects and other advantages of the disclosed subject matter will be readily apparent to one skilled in the art to which the disclosure pertains from a perusal or the claims, the appended drawings, and the following detailed description of the preferred embodiments.